Zimbra as an accout hub for email and calendar

Hi,
i am new here, so hi everybody.

I am a consultant and have several clients. Each client has a seperate exchange account for me, and they like to use that one only, including the calendar of their domain. Kind of annoying, but oh well...
I have been looking for a solution to replace outlook and stumbled upon zimbra.

I downloaded the zimbra desktop client, and was thrilled with the features of how I was able bundle all of my accounts (especially email AND calendar) in the client. I simply signed up all of the exchange accounts, and voila, it all worked!!! So I want to use zimbra as an account hub.

Then I figurd, it would be the best idea to get a zimbra server, so I have all of this bundeling online, rather than on each device seperatly. After signing up to a few hosted trial ones, i realized, that this does not seem possible.

If I were to get a zimbra server (for my company) though, would I be able to get this done? (remeber, i cant change DNS or MX records, but need to sign into other exchange accounts)